The Related Extension and Application of the Ši'lnikov Theorem
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-03-18
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
The traditional Ši'lnikov theorems provide analytic criteria for proving the existence of chaos in high-dimensional autonomous systems.
We have established one extended version of the Ši'lnikov homoclinic theorem and have given a set of sufficient conditions under which the system generates chaos in the sense of Smale horseshoes.
In this paper, the extension questions of the Ši'lnikov homoclinic theorem and its applications are still discussed.
We establish another extended version of the Ši'lnikov homoclinic theorem.
In addition, we construct a new three-dimensional chaotic system which meets all the conditions in this extended Ši'lnikov homoclinic theorem.
Finally, we list all well-known three-dimensional autonomous quadratic chaotic systems and classify them in the light of the Ši'lnikov theorems.
American Psychological Association (APA)
Chen, Baoying. 2013. The Related Extension and Application of the Ši'lnikov Theorem. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-5.
https://search.emarefa.net/detail/BIM-460533
Modern Language Association (MLA)
Chen, Baoying. The Related Extension and Application of the Ši'lnikov Theorem. Journal of Applied Mathematics No. 2013 (2013), pp.1-5.
https://search.emarefa.net/detail/BIM-460533
American Medical Association (AMA)
Chen, Baoying. The Related Extension and Application of the Ši'lnikov Theorem. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-5.
https://search.emarefa.net/detail/BIM-460533
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-460533